Chirality
geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or more particularly can't be mapped to its mirror images by rotations and translations alone. Such objects then come in two forms, called enantiomorphs. The word chirality is derived from the greek χειρ (cheir), the hand, the most familiar chiral object; the word Enantiomorph stems from the greek εναντιος (enantios) 'opposite' and μορφη (morphe) 'form'. A non-chiral figure is also called achiral.
A figure is achiral if and only if its symmetry group contains at least one indirect (orientation reversing) isometry.
For a discussion of chiral molecules or atoms or chirality in chemistry, see the section under Chemistry below.
Many familiar objects are chiral - for instance, a right glove and left glove are enantiomorphic, and so are the S and Z tetrominoes of the popular video game Tetris.
In three dimensions, every figure which possesses a plane of symmetry or a center of symmetry is achiral. (A center of symmetry of a figure <math>F<math> is a point <math>C<math>, such that <math>F<math> is invariant under the mapping <math>x\mapsto -x<math>, where we have chosen <math>C<math> to be the origin of the coordinate system.) Note, however, that there are achiral figures lacking both plane and center of symmetry.
In two dimensions, every figure which possesses a line of symmetry is achiral, and it can be shown that every bounded achiral figure must have a line of symmetry. Consider the following pattern:
> > > > > > > > > >
> > > > > > > > > >
This figure is chiral, as it is not identical to its mirror image:
> > > > > > > > > >
> > > > > > > > > >
But if one prolongs the pattern in both directions to infinity, one receives an (unbounded) achiral figure which has no line of symmetry.
Chemistry
In chemistry (especially organic chemistry), a molecule is chiral (and said to have chirality) if its overall structure and overall three-dimensional configuration is always chiral in accordance with the preceding geometric definition regardless of how the molecule is conformed. Conformations are temporary positions a molecule can assume as a result of bond rotation, bending, or stretching as long as a bond is not broken to change the molecule.
An atom is often said to be chiral if the atom is a chiral center in a molecule. An atom is a chiral center when the molecule it is in, regardless of the molecule's conformation, can't be made to be identical to (or super-imposable on) its mirror image by rotations and translations alone if the chiral atom's center must be super-imposable on its own mirror image position. A molecule can have multiple chiral centers without being chiral overall. Also, it is possible, but not very common, for a molecule to have a local area that is not an atom that acts effectively as a chiral center anyway due to an unusual shape the molecule may have. It is also possible for a molecule's overall shape to be chiral without any specific chiral center points in the molecule. An example is given by 1,3-dichloro-allen, characterized by 2 double bonds on the same carbon, outlining two perpendicular planes. For this molecule it is possible to write two enantiomers even if it lacks a chiral center.
Molecular isomers that are enantiomorphs of each other are called enantiomers. Because such molecules typically show optical activity, they are also often called optical isomers, The study of chiral molecules, enantiomers (optical isomers), and molecules with chiral atoms is part of the science of stereochemistry.
Physics
The fundamental laws of physics may be chiral, as the weak charge is not invariant under a reflection unless particles are replaced by their antiparticles as well, and kaon decay appears to violate even that symmetry.
Chirality appears to be important in particle physics because the universe seems to be asymmetric as far as spin is concerned.
Imagine a particle moving in the direction of one's thumb.
The particle can be classified as left-handed if it is spinning in the direction of the fingers of the left-hand and right-handed if it is spinning in the direction of the fingers of the right-hand.
Up to now, only left-handed neutrinos (and right-handed anti-neutrinos) have been observed.
But this is explained by the difficulty of detecting right-handed particles at extremely small masses.
See also
